Some Mann-Type Implicit Iteration Methods for Triple Hierarchical Variational Inequalities, Systems Variational Inequalities and Fixed Point Problems

Lu-Chuan Ceng and Xiaoye Yang
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Lu-Chuan Ceng: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Xiaoye Yang: Department of Mathematics, Ren’ai College, Tianjin University, Tianjin 301636, China

Mathematics, 2019, vol. 7, issue 3, 1-20

Abstract: This paper discusses a monotone variational inequality problem with a variational inequality constraint over the common solution set of a general system of variational inequalities (GSVI) and a common fixed point (CFP) of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping in Hilbert spaces, which is called the triple hierarchical constrained variational inequality (THCVI), and introduces some Mann-type implicit iteration methods for solving it. Norm convergence of the proposed methods of the iteration methods is guaranteed under some suitable assumptions.

Keywords: mann-type implicit iteration methods; triple hierarchical constrained variational inequality; general system of variational inequalities; strong convergence; hilbert spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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